In this paper we prove a general result concerning continuity of the blow-up time and the blow-up set for an evolution problem under perturbations. This result is based on some convergence of the perturbations for times smaller than the blow-up time of the unperturbed problem together with uniform bounds on the blow-up rates of the perturbed problems. We also present several examples. Among the...

Let X be a complex analytic space and let f :X → C be a proper complex analytic function with nonsingular generic fibres. By adapting the blowanalytic methods of Kuo we construct a retraction of a neighbourhood of the central fibre f(0) onto f(0). Our retraction is defined by the flow of a real analytic vector field on an oriented real analytic blow-up of X . Then we describe in terms of this b...

We study the blow-up of the solution to a quasilinear viscoelastic wave system coupled by nonlinear sources. The system is of homogeneous Dirichlet boundary condition. The nonlinear damping and source are added to the equations. We assume that the relaxation functions are non-negative non-increasing functions and the initial energy is negative. The competition relations among the nonlinear prin...

Using a Fourier spectral method, we provide a detailed numerical investigation of dispersive Schrödinger-type equations involving a fractional Laplacian in an one-dimensional case. By an appropriate choice of the dispersive exponent, both mass and energy sub- and supercritical regimes can be identified. This allows us to study the possibility of finite time blow-up versus global existence, the ...

We use techniques from reaction-diffusion theory to study the blow-up and existence of solutions of the parabolic Monge–Ampère equation with power source, with the following basic 2D model 0.1 (0.1) ut = −|Du|+ |u|u in R × R+, where in two-dimensions |D2u| = uxxuyy − (uxy) and p > 1 is a fixed exponent. For a class of “dominated concave” and compactly supported radial initial data u0(x) ≥ 0, th...

‎In this paper‎, ‎we consider the existence and uniqueness of the global solution for the sixth-order damped Boussinesq equation‎. ‎Moreover‎, ‎the finite-time blow-up of the solution for the equation is investigated by the concavity method‎.

Abstract Solutions to nonlinear Schrödinger equations may blow up in finite time. We study the influence of the introduction of a potential on this phenomenon. For a linear potential (Stark effect), the blow-up time remains unchanged, but the location of the collapse is altered. The main part of our study concerns isotropic quadratic potentials. We show that the usual (confining) harmonic poten...

We construct blow-up solutions of the energy critical wave map equation on R → N with polynomial blow-up rate (t for blow-up at t = 0) in the case when N is a surface of revolution. Here we extend the blow-up range found by Carstea (ν > 1 2 ) based on the work by Krieger, Schlag and Tataru to ν > 0. This work relies on and generalizes the recent result of Krieger and the author where the target...